which of the following are Muiltset operations
Answers
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In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The positive integer number of instances, given for each element is called the multiplicity of this element in the multiset. As a consequence, an infinite number of multisets exist, which contain only elements a and b, but vary by the multiplicity of their elements:
- The set {a, b} contains only elements a and b, each having multiplicity 1 when {a, b} is seen as a multiset.
- In multiset {a, a, b}, the element a has multiplicity 2, and b has multiplicity 1.
- In multiset {a, a, a, b, b, b}, a and b both have multiplicity 3.
These objects are all different, when viewed as multisets, although they are the same set, since they all consist of the same elements. As with sets, and in contrast to tuples, order does not matter in discriminating multisets, so {a, a, b} and {a, b, a} denote the same multiset. To distinguish between sets and multisets, a notation that incorporates square brackets is sometimes used: the multiset {a, a, b} can be denoted as [a, a, b]
Answer:
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Explanation:
Explanation:In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The positive integer number of instances, given for each element is called the multiplicity of this element in the multiset. As a consequence, an infinite number of multisets exist, which contain only elements a and b, but vary by the multiplicity of their elements:
Explanation:In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The positive integer number of instances, given for each element is called the multiplicity of this element in the multiset. As a consequence, an infinite number of multisets exist, which contain only elements a and b, but vary by the multiplicity of their elements:The set {a, b} contains only elements a and b, each having multiplicity 1 when {a, b} is seen as a multiset.
Explanation:In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The positive integer number of instances, given for each element is called the multiplicity of this element in the multiset. As a consequence, an infinite number of multisets exist, which contain only elements a and b, but vary by the multiplicity of their elements:The set {a, b} contains only elements a and b, each having multiplicity 1 when {a, b} is seen as a multiset.In multiset {a, a, b}, the element a has multiplicity 2, and b has multiplicity 1.
Explanation:In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The positive integer number of instances, given for each element is called the multiplicity of this element in the multiset. As a consequence, an infinite number of multisets exist, which contain only elements a and b, but vary by the multiplicity of their elements:The set {a, b} contains only elements a and b, each having multiplicity 1 when {a, b} is seen as a multiset.In multiset {a, a, b}, the element a has multiplicity 2, and b has multiplicity 1.In multiset {a, a, a, b, b, b}, a and b both have multiplicity 3.
Explanation:In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The positive integer number of instances, given for each element is called the multiplicity of this element in the multiset. As a consequence, an infinite number of multisets exist, which contain only elements a and b, but vary by the multiplicity of their elements:The set {a, b} contains only elements a and b, each having multiplicity 1 when {a, b} is seen as a multiset.In multiset {a, a, b}, the element a has multiplicity 2, and b has multiplicity 1.In multiset {a, a, a, b, b, b}, a and b both have multiplicity 3.These objects are all different, when viewed as multisets, although they are the same set, since they all consist of the same elements. As with sets, and in contrast to tuples, order does not matter in discriminating multisets, so {a, a, b} and {a, b, a} denote the same multiset. To distinguish between sets and multisets, a notation that incorporates square brackets is sometimes used: the multiset {a, a, b} can be denoted as [a, a, b]